I think this is factually incorrect, and I'll explain why.

Firstly, for humidity, it doesn't matter what your water reservoir is.   I have done tests on sealed fruiting chambers with a digital  hygrometer.   You don't need a humidifier, ultrasonic or otherwise.   If there's anything wet inside the FC, then humidity will be >99%, and will stay that way for weeks.   In fact, if there's anything at all wet in the FC, you won't be able to get the humidity under 99%.   Doesn't matter whether it's vermiculite, perlite, or even a puddle of standing water.   Even if it's just a single wet sock, it will keep the humidity up for 3 days even with fanning several times a day.  If you don't believe it, test yourself with a calibrated digital hygrometer.

Vermiculite holds LIQUID better than Perlite does.   That doesn't mean water won't evaporate from vermiculite.   Contrary to the article above, just because Perlite has holes in it doesn't mean it has more surface area than verm.  Vermiculite has smaller granule size which means it actually has about the same surface area is perlite.   It releases water just as well, and has a higher capacity.

The best way to keep moisture up in the fruiting chamber is to use a half inch of vermiculite soaked to 100% of field capacity.   No misting needed.   Add water directly to the vermiculite layer.  Maintain it so that the surface of the verm appears wet, but if you dig to the bottom with your finger, you see a very thin standing layer of water at the bottom of the container.   This keeps the humidity nearly at 100%.   It also provides a wicking layer so that water can wick up through the verm into your BRF cakes or spawn, which is the best way for them to get water. 

I've just harvested 120g off a first flush of PF cakes sitting on fully hydrated vermiculite, so I can vouch for its effectiveness.   As for the article above, it doesn't even reference any outside sources to back up its claim that Perlite is better for humidifying, doesn't demonstrate any tests, basically it all just sounds like hearsay digested from the forums here.

What is the role of Perlite in mushroom cultivation?   Not much.  Perlite is for aeration and drainage.   Verm is already loose and doesn't need to be aerated.   Cultivated mushrooms are watered carefully, they aren't exposed to rainstorms, so drainage is not a factor.    Perlite can be used for PF cakes though it won't hold as much moisture and thus will result in smaller fruits.   It can loosen up a dense casing or spawn layer, but why would you make it that dense in the first place?   Perlite is for cultivating green plants, not mushrooms.